Yes
$\rightarrow$ is have Precedence, but it is not associative,i think.
But $P\rightarrow Q\rightarrow R$ what is the answer?
if you take $\rightarrow$ is Left associative,then $(P\rightarrow Q)\rightarrow R$
(or)
if you take $\rightarrow$ is Right associative,then $P\rightarrow (Q\rightarrow R)$
Both cases answer might be different.